% This project is a template slides for the subsequent presentations which are significant during the postgraduate period.
% Template for College of Information Science and Electronic Engineering, Zhejiang University.
% Compiled with pdflatex.
% By Xue Shengke.
% The bib for this template is bibtex not biber

\documentclass[10pt, mathserif]{beamer}	% font and size
\mode<presentation>
{
	\setbeamercovered{dynamic}	% translucent when using pause
	\setbeamertemplate{navigation symbols}{}	% hide navigation bars
	\setbeamertemplate{caption}[numbered]	% numerate captions
	% \setbeamertemplate{background}{\includegraphics[height=\paperheight]{ISEE.pdf}}	% set background image
	\setbeamertemplate{footline}{\textcolor{light-gray}{\scriptsize \insertframenumber/\inserttotalframenumber} \hfill}	% display page number at bottom left corner	
}
\usepackage{ctex}
% \usepackage{xeCJK}
\usepackage{times}		% font for english, Times New Roman
\usepackage{amsmath, amsfonts, amssymb}	% math equations, symbols
\usepackage[english]{babel}
\usepackage{color}		% color content
\usepackage{graphicx}	% import figures
\usepackage{subfigure}
\usepackage{url}		% hyperlinks
\usepackage{bm}			% bold type for equations
\usepackage{hyperref}
\hypersetup{hypertex=true,
            colorlinks=true,
            linkcolor=blue,
            anchorcolor=blue,
			citecolor=blue}
\usepackage{multirow}
\usepackage{listings}
\usepackage{xcolor}
% \setCJKsansfont{黑体}	% all Chinese should be enclosed between the commands

% set font
\setCJKfamilyfont{yh}{Microsoft YaHei}

% set line space
\linespread{1.5}

\newcommand{\ftitle}[1]{\frametitle{#1}}	% userdefine frametitle
\definecolor{light-gray}{gray}{0.90}

\graphicspath{{figure/}}	% set graph path

% special for time line
\usepackage[utf8]{inputenc}
\usepackage[TS1,T1]{fontenc}
\usepackage{array, booktabs}
% \usepackage[x11names]{xcolor}
\usepackage{colortbl}
\usepackage{caption}
\definecolor{baseD}{HTML}{7CAFC2}
%baseD是一个很柔和的蓝色，你可以在相关github主页找到base16色的图样。
\newcommand{\foo}{\color{baseD}\makebox[0pt]{\textbullet}\hskip-0.5pt\vrule width 1pt\hspace{\labelsep}}

% 设置超链接
\hypersetup{hidelinks}
\def\equationautorefname        {式}
\def\footnoteautorefname        {脚注}
\def\figureautorefname          {Figure}
\def\tableautorefname           {表}
\def\partautorefname            {篇}
\def\chapterautorefname         {章}
\def\sectionautorefname         {节}
\def\subsectionautorefname      {小节}
\def\subsubsectionautorefname   {小小节}
\def\paragraphautorefname       {段落}
\def\subparagraphautorefname    {子段落}
\def\appendixautorefname        {附录}
\def\FancyVerbLineautorefname   {行}
\def\theoremautorefname         {定理}
\def\listoffigures              {代码}
\def\lstlistingname             {代码}

% 代码格式和颜色定义
% \definecolor{dkgreen}{rgb}{0,0.6,0}
% \definecolor{gray}{rgb}{0.5,0.5,0.5}
% \definecolor{comment}{rgb}{0.56,0.64,0.68}
% \lstset{
%   frame=tb,
%   aboveskip=3mm,
%   belowskip=3mm,
%   xleftmargin=2em,
%   xrightmargin=2em,
%   showstringspaces=false,
%   columns=flexible,
%   framerule=1pt,
%   rulecolor=\color{gray!35},
%   backgroundcolor=\color{gray!5},
%   basicstyle={\small\ttfamily},
%   numbers=left,
%   numberstyle=\tiny\color{gray},
%   keywordstyle=\color{blue},
%   commentstyle=\color{comment},
%   stringstyle=\color{dkgreen},
%   breaklines=false,
%   breakatwhitespace=true,
%   tabsize=2,
% }

\usepackage{fancybox}
\usepackage{xcolor}
\usepackage{times}
\usepackage{listings}

\usepackage{booktabs}
\usepackage{colortbl}

\newcommand{\Console}{Console}
\definecolor{mygreen}{rgb}{0,0.6,0}
\definecolor{mymauve}{rgb}{0.58,0,0.82}
\definecolor{mygray}{gray}{.9}
\definecolor{mypink}{rgb}{.99,.91,.95}
\definecolor{mycyan}{cmyk}{.3,0,0,0}
\lstset{ %
	backgroundcolor=\color{white},   % choose the background color
	basicstyle=\footnotesize\rmfamily,     % size of fonts used for the code
	columns=fullflexible,
	breaklines=true,                 % automatic line breaking only at whitespace
	captionpos=b,                    % sets the caption-position to bottom
	tabsize=4,
	commentstyle=\color{mygreen},    % comment style
	escapeinside={\%*}{*)},          % if you want to add LaTeX within your code
	keywordstyle=\color{blue},       % keyword style
	stringstyle=\color{mymauve}\ttfamily,     % string literal style
	numbers=left, 
	%	frame=single,
	rulesepcolor=\color{red!20!green!20!blue!20},
	% identifierstyle=\color{red},
	language=c
}
\usetheme{Frankfurt}

\def\R{\mathbb{R}}
\def\E{\mathbb{E}}
\def\st{\text{s.t.\ }}
\def\dom{\text{dom}}
\def\1{\textbf{1}}
\def\argmin{\text{argmin}}
\def\argmax{\text{argmax}}


\captionsetup[figure]{labelformat={default},labelsep=period,name={图.}}

\title[abbreviation]{矩阵论大作业}
\author{何扬槊 3180102687}
\institute[ISEE]{\normalsize 
		\includegraphics[width=0.2\textwidth]{ZJU_BLUE.pdf}  \\  % add a special logo on cover page
	College of Information Science and Electronic Engineering \\
	信息与电子工程学院 \\
	Zhejiang University \\
	浙江大学
	}
	\date{\today}
	
\begin{document}
\begin{frame}
	\titlepage	% make the cover page here
\end{frame}
	

\AtBeginSection[]
{
\begin{frame}
   	\ftitle{Outline}		% contents for better review
    \tableofcontents[currentsection, currentsubsection]
\end{frame}
}


\section{Simulation}

\begin{frame}[fragile]{code1}
	\frametitle{Matlab计算}
	根据推导可以直接利用matlab计算
	\lstinputlisting[lastline=11,
	language=matlab,
	frame=single,
	caption=matlab 计算$\vec{c}_{MV}$最优解,
	label=matlab]
	{./code/code1.m}

\end{frame}

\begin{frame}
	\frametitle{Matlab计算}
	取对角得对应角度功率 \\
	$\theta = \theta_0,\ \theta_1,\cdots,\theta_{NUM}$
	\begin{equation*}
		\left(
		\begin{array}[]{ccc}
			y_1(\theta_0) & \cdots & y_{Ns}(\theta_{0}) \\
			y_1(\theta_{1}) & \cdots & y_{Ns}(\theta_{1}) \\
			\vdots &  & \vdots \\
			y_1(\theta_{NUM}) & \cdots & y_{Ns}(\theta_{NUM}) \\
			
		\end{array}
		\right)
		\left(
		\begin{array}[]{cccc}
			y_1(\theta_0) & y_1(\theta_1) & \cdots & y_1(\theta_{Num}) \\
			y_2(\theta_{0}) & y_2(\theta_{1}) & \cdots & y_2(\theta_{Num}) \\
			\vdots & \vdots & & \vdots \\
			y_{Ns}(\theta_{0}) & y_{Ns}(\theta_{1}) & \cdots & y_{Ns}(\theta_{NUM}) \\
			
		\end{array}
		\right)
	\end{equation*}
	\begin{equation*}
		=\left(
		\begin{array}[]{cccc}
			\sum\limits_{i=1}^{Ns}y_i^2(\theta_0) & \sum\limits_{i=1}^{Ns}y_i(\theta_0)y_i(\theta_1) & \cdots & \sum\limits_{i=1}^{Ns}y_i(\theta_0)y_i(\theta_{NUM}) \\
			\sum\limits_{i=1}^{Ns}y_i(\theta_1)y_i(\theta_0) & \sum\limits_{i=1}^{Ns}y_i^2(\theta_1) &\cdots& \sum\limits_{i=1}^{Ns}y_i(\theta_1)y_i(\theta_{NUM}) \\
			\vdots & \vdots & & \vdots \\
			\sum\limits_{i=1}^{Ns}y_i(\theta_{NUM})y_i(\theta_0) & \sum\limits_{i=1}^{Ns}y_i(\theta_{NUM})y_i(\theta_1) & \cdots & \sum\limits_{i=1}^{Ns}y_i^2(\theta_{NUM}) \\
			
		\end{array}
		\right)
	\end{equation*}
	
\end{frame}

\begin{frame}
	\frametitle{仿真结果}
	在$\theta_0 = 30^\circ,\ SNR = 20dB$时，为清晰地对比两张方法的优劣，将两个功率图合并到如图\autoref{fig:Comp30}
	\begin{figure}[H]
		\centering
		\includegraphics[width=7cm]{Comp30}
		\caption{两种方法对比图}
		\label{fig:Comp30}
	\end{figure}
	

\end{frame}

\section{Property}

\begin{frame}
	\frametitle{SNR对DOA估计的影响}
	设置SNR分别为$-20dB,\ -10dB,\ -3dB,\ 3dB,\ 10dB,\ 20dB$，可以得到如\autoref{fig:SNR}结果，低信噪比时，两种方法的估计效果均较差，但是高信噪比时，CBF方法主瓣以及旁瓣几乎没有改变；而MVDR方法的主瓣愈加明显。
	% 随着信噪比的改变，CBF方法主瓣以及旁瓣几乎没有改变；而MVDR方法中，信噪比越大，其主瓣越明显，越容易判断其波束方向。
	\begin{figure}[H]
		\vspace{-1.2cm}
		\centering
		\subfigure[CBF]{
		\begin{minipage}[t]{0.5\linewidth}
		\centering
		\label{fig:CBF_SNR}
		\includegraphics[width=5cm]{CBF_SNR}
		\end{minipage}%
		}%
		\subfigure[MVDR]{
		\begin{minipage}[t]{0.5\linewidth}
		\centering
		\label{fig:MVDR_SNR}
		\includegraphics[width=5cm]{MVDR_SNR}
		\end{minipage}%
		}%
		\caption{CBF与MVDR方法不同信噪比的功率图}
		\label{fig:SNR}
	\end{figure}
	

\end{frame}









\begin{frame}
	\frametitle{提问}
	\qquad \qquad \qquad \qquad \qquad \qquad \qquad 提问
	

\end{frame}


\end{document}
